Question

spheres A and B have their radii 40cm and 10cm respectively. Find the ratio of the surface area of A to the surface area of B

Answer 1

surface area of sphere = 4× pi × r^2
ratio = surface area of a sphere /surface area of the sphere
= 4 × 3.14 × 40 × 40 / 4 × 3.14 × 10× 10
= 40 × 40 / 10× 10
= 4 × 4 / 1 × 1
= 16 / 1
Ratio = 16 : 1

Answer 2

The ratio of the surface area of A to the surface area of B is 16 : 1.

Given:

Radius of sphere A , $r_1$ = 40 cm

Radius of sphere B ,$r_2$ = 10 cm

To find : The ratio of the surface area of A to the surface area of B

Formula used:

The surface area of the sphere = 4πr²

Here, r is the radius of a sphere.

Solution:

Step1: Find the surface area of sphere A and sphere B:

$r_1 = 40 \ cm$ and $r_2 = 10 \ cm$

Surface area of sphere A = $4 \pi r_1^2$

Surface area of sphere A = 4π × (40)²

Surface area of  sphere A = 4π × 1600

Surface area of sphere B = $4 \pi r_2^2$

Surface area of sphere B = 4π × (10)²

Surface area of  sphere B = 4π × 100

Step 2: Find the ratio of the surface area of A to the surface area of B:

Surface area of A : surface area of B

4π × 1600 : 4π × 100

1600 : 100

16 : 1

Hence, the ratio of the surface area of sphere A to the surface area of sphere B is 16 : 1.

 

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